As optical fiber communications systems proliferate, the problem of interconnecting optical components having unequal modal spot sizes assumes increasing importance. Such interconnections are required in a variety of circumstances including: 1) the interconnection of laser sources to fibers, 2) the interconnection of two fibers having dissimilar modal properties, and 3) the interconnection of fibers to waveguides and waveguides to fibers. Such interconnections have been an area of active research, and a variety of approaches have been developed. For example, pre-tapered preforms have been prepared to draw tapered regions for connecting lasers to fibers. J. Armitay et al., J. Lightwave Technol. LT-5, 70 (1987). Fibers have been tapered through capillaries in order to achieve beam-expansion. K. P. Jedrzejewski, 22 Electron. Lett. 106 (1986) and fiber cores have been thermally expanded for splicing dissimilar fibers. S. G. Kosinski et al., Proc. Optical Fiber Communications Conference OFC, Paper Th16, 231 (1992). These techniques, however, all depend on control of the physical dimensions of the fiber core-a control which is difficult and expensive to achieve. Accordingly, there is a need for improved waveguiding structures for transforming an optical beam of a first modal spot size to a beam of a second modal spot size.